LOS ANGELES, California (CNN) --After returning to the United States, the American bounty hunter who nabbed fugitive cosmetics heir Andrew Luster in Mexico last month bucked his gritty, weathered image Wednesday and choked up as he described capturing the man he called an international rapist.

Bounty hunter Duane "Dog" Chapman said the people of Mexico thanked him personally for capturing Luster two weeks ago in Puerta Vallarta.

Chapman's gravelly voice broke at a news conference when he described finally capturing Luster, and he illustrated his point with a lyric from the rap star Eminem.

"There's a song by Eminem that says, 'Take the moment. It's your chance,'" said Chapman, garbed in a fringed leather poncho. "We had to protect everyone (from Luster), we thought."

Chapman never explained how he, his brother and son were allowed to travel back to the United States. Charged in Mexico with unlawfully detaining Luster, the three were out on bail and required to obtain a judge's permission to travel outside the Mexican state of Jalisco.

The judge in the case never signed any such papers, said Marco Roberto Suarez, the supervising prosecutor for Jalisco.

Chapman was required to check in daily with Mexican immigration authorities, and with the judge in the case every Monday, Suarez said. If the Chapmans do not appear for their regularly scheduled check-in Thursday, then prosecutors will ask the judge to demand that the Chapmans comply with their bail agreement, and they may seek an arrest warrant, Suarez said.

Should the trio fail to show up for next Monday's appearance before the judge, they would likely be declared fugitives and Mexican officials would seek to have the Chapmans returned to Mexico to face trial, Suarez said.

"My lawyers in Mexico are working on all the legal issues concerning my return to the United States," Chapman told reporters. "Because my attorneys are involved as we speak right now, I'm sure the Mexican authorities will resolve this matter to go my way."

Duane "Dog" Chapman in a Puerta Vallarta jail before his release.

The Chapmans' arrest, along with Luster, shortly after they caught the Max Factor heir was a twist to the bounty hunter's long-stated ambition to capture the fugitive.

"We were surprised," Chapman said.

He said he regretted running afoul of Mexican law while trying to bring Luster to justice, but he said he didn't think he ever broke the law.

Mexican police said the three men, working with a two-man camera crew, struggled with and subdued Luster outside a nightclub, put him in a vehicle and drove off with him June 18. Soon afterward, Mexican police stopped two SUVs carrying the men and took them all into custody.

Attorneys for Chapman told CNN that he and the four others had come to Mexico on vacation, not for the purpose of arresting Luster. The five happened to be out one night dining when they spotted and recognized Luster, and they decided to apprehend him, the attorneys said.

Luster, the great-grandson of cosmetics tycoon Max Factor, fled California in January in the middle of his trial on 86 counts stemming from the rapes of three women who were incapacitated with GHB, the "date rape" drug. At the time, he was free on $1 million bond.

After his disappearance, the jury convicted him in absentia, and he was sentenced to 124 years in prison. He was returned to California last Thursday and is now at the Salinas Valley State Prison, where he'll serve his sentence.

Luster will not be eligible for parole for 104 years, said Maeve Fox, the deputy district attorney in Ventura County, California, who prosecuted Luster.

Andrew Luster is now serving his prison sentence in California.

Luster's attorney is appealing his conviction and is seeking a return of the $1 million bail, Fox said.

Chapman, who claims to have captured more than 6,000 fugitives during his career, began tracking Luster the day after he disappeared, hoping to claim some of the proceeds from the forfeited bond. Mexican officials, however, said he was not authorized to track Luster and take him into custody in Mexico.

"In my opinion," Chapman said in a statement released Wednesday, "he (Luster) is a sexual predator who did terrible things to women in America, and I believe he was doing the same thing to women in Mexico."

Fox said she is thankful the fugitive has been caught, but doesn't condone Chapman's practices.

"We wish he had complied with local [Mexican] law enforcement and the FBI," she said.